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平截面方法导出轧制力方程的一般形式是P=Hl′Q_Pξ。这四个因子可以独立地处理。 重点研究了应力状态系数Q_P的模型。从三次的实验结果,发现了即便对于板带冷轧,当l′/h小于一定值时,也会出现宏观的不均匀压下,平截面法得到的Q_P理论解不适用,应给以修正量ΔQ_P∞1/(l′/h). 共给出三种方案的Q_P模型: (1)分段统计分析的结果: 1)l′/h<4.2,Q~P=1.7025-0.0402 (R′/H)~(1/2)-0.1972γ (R′/H)~(1/2) l′/h≥4.2,Q_P=0.9599+0.0130(R′/H)~(1/2)+0.0254γ (R′/H)~(1/2) 2)Q_P=1.08+1.79μγ(R′/H)~(1/2)-1.02γ l′/h<4.2,μ=0.0917+10.6017/(ε)~2 l′/h≥4.2,μ=0.1059-0.0005ε (2)同时考虑均匀与不均匀变形的结果; U_P=0.6859-0.4962γ+0.0099 (R′/H)~(1/2)+0.1025γ(R′/H)~(1/2)+1.298(h/l′)或 Q_P=0.6903-0.5025γ+0.0572(l/h)+0.0186γ(l/h)+1.29(h/l′) (3)考虑出口弹性回复区对轧制压力的贡献: 1)Q_P~*=0.4364-0.1350γ+0.0229(R′/H)~(1/2)+0.0868γ(R′/H)~(1/2)+1.5 h/l′ 2)Q_P~*=1.08+1.79μ~*γ(R′/H)~(1/2)-1.02γ μ~*=0.0356/((l′/h)-2.503)+0.0559、 对多品种产品的轧机,它会有更好的适应性,但使计算复杂。 方案(2)的方程结构物理概念明确,对观测值有

The model of rolling force coefficient Q_P has been studied. Three trials oftest showed that macroscopic inhomogeneous draft may occur in the cold rollingof sheets and strips if the parameter l′/h is less than a certain value. The coeffi-cient Q_P given by "slab theory" does not seem proper, and should be modifiedby an amount of ΔQ_P∝(l′/h)~(-1). Three programs of Q_P model are suggested: Ⅰ. for different regions of the parameter l′/ha) l′/h<4.2, Q_P=1.7025-0.0402(R′/H)~(1/2)-0.1972γ(R′/H)~(1/2) l′/h≥4.2, Q_P =0.9599+0.0130(R′/H)~(1/2)+0.0254γ(R′/H)~(1/2)b) Q_P=1.08+1.79μγ(R′/H)~(1/2)-1.02γ l′/h<4.2, μ=0.0917+10.6017/(ε)~2 l′/h≥4.2, μ=0.1059-0.0005ε Ⅱ. taking into account both homogeneous and inhomogeneous deformation Q_P=0.6859-0.4962γ+0.0099(R′/H)~(1/2)+0. 1025γ(R′/H)~(1/2)+1.298h/l′ or Q_P=0.6903-0.5025γ+0.0572l′/h+0.0186γl′/h+1.29h/l′ Ⅲ. taking into account the output elastic recovery contributing to roll-force a) Q_P~*=0.4364-0.1350γ+0.0229(R′/H)~(1/2)+0.0868γ(R′/H)~(1/2)+1. 54h/l′ b) Q_P~*=1.08+1.79μ~*γ(R′/H)~(1/2)-1.02γwhere μ~*=0.0356/(l′/h-2.503)+0.0559 The parameter Q_P~* seems to be more suitable for the mill of most productsbut the relevant computation is more complicated. The physical idea of the equations in program Ⅱ is explicit and the roll-forcethus estimated has been found to agree very closely with the experimental data.It is recommended for the rolling of either cold or hot strips as well as heavyplates. From the results of off-line simulation, however, the accuracy of the modelmay be substantially improved by the combination of the adaptive control to latterpasses of a coil with that to the same pass of the mext coil using the programof the exponential smoothing method, the error can be reduced to within 10%.